The difference in the genealogies is that of St. Joseph versus the Blessed Virgin Mary, with Lukes account that of the BVM. They were both of the line of David.

I agree. However, Mary is not mentioned. Not only that, but the genitive case for of in the Greek indicates a father-son relation. If you read a literal translation of the Greek text, it says this, with the word son implied because of the Greek case :

And Jesus himself was beginning to be about thirty years of age, being, as was supposed, son of Joseph, the [son] of Eli, the [son] of Matthat, the [son] of Levi, the [son] of Melchi, the [son] of Janna, the [son] of Joseph, the [son] of Mattathias, .... (Luke 23-38 YLT).

So what are we to make of this?

I don't know. There has been much debate on the geneaologies over the centuries. Some take it that Mary's father was named Heli, and that the genealogy is referring to Joseph as his son in law. That belief is consistent with Greek usage and thus separates it from Joseph's genealogy in Matthew.

I'm with you on the genealogy of Luke being Mary's genealogy. One thing we do know is that in a time and place where genealogies were carefully kept and managed, we have no indication that Jesus's geneaology was ever challenged.

However, this still doesn't resolve the genealogical differences between Matthew and 1 Chronicles.